Relatively compact subset

This article defines a property over pairs of a topological space and a subspace, or equivalently, properties over subspace embeddings (viz, subsets) in topological spaces

Definition

A subset of a topological space is termed relatively compact if its closure in the space is compact.

Note that when the space is a Hausdorff space, or more generally, a KC-space, it suffices to say that the subset is contained in a compact subset. (The equivalence of definitions relies on the fact that a closed subset of a compact space is compact and a compact subset of a Hausdorff space is closed).